what is the value of sin^2(π÷10)+sin^2(4π÷10)+sin^2(6π÷10)+sin^2(9π÷10)
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12
Answer:
2
Step-by-step explanation:
sin²(π÷10) + sin²(4π÷10) + sin²(6π÷10) + sin²(9π÷10)
=sin²(π÷10) + sin²(4π÷10)+sin²(5π÷10+π÷10 ) + sin²(5π÷10+4π÷10)
=sin²(π/10) + sin²(4π/10) + sin²(π/2+π/10 ) + sin²(π/2+4π/10)
=sin²(π/10) + sin²(4π/10)+cos²(π/10) + cos²(4π/10)
=sin²(π/10) +cos²(π/10) + sin²(4π/10)) + cos²(4π/10)
=1+1
=2
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